Pedro Lacerda's homepage

The Sun-KBO-Earth angle, known in solar system astronomy as phase angle, oscillates as the Earth orbits the Sun.

When the KBO is in opposition, the phase angle is minimum. It will be zero if the KBO orbit has zero inclination.

When the KBO is in quadrature, the phase angle is maximum.

Assuming the KBO is static, the phase angle alpha is given by

alpha = arccos( (a - cos(i) cos(2 pi t)) / ( sqrt(1 + a^2 - 2 a cos(i) cos(2 pi t)) ) )

where a is the KBO semi-major axis in au, i is the angle between the Sun-KBO line and the ecliptic plane and t is time in years from opposition. All angles are in radians.

The equation above is plotted below for different combinations of a and i.